Multiplying Polynomials Worksheet

A polynomial is an algebraic expression consisting of variables and coefficients. We can perform various operations on polynomials, including addition, subtraction, multiplication, and division. This worksheet focuses on multiplying polynomials using different methods.

Read More: Multiplying Polynomials

Practice Questions on Polynomial Multiplication

Below are some solved examples:

Question 1: Evaluate 100pq × 4qr × 8pr  

Solution:

Given: 100pq × 4qr × 8pr  

So, we shall first multiply 100 pq and 4qr = 400pq²r

Now multiply this product with 8pr  

Final product is 400pq²r × 8pr = 3200p²q²r²

We can obtain the same solution by first multiplying the coefficients 100 × 4 × 8 = 3200

The product of algebraic coefficients is pq × qr × pr = p²q²r²

So, the final product is 3200p²q²r²

Question 2: Find 5pqr × 10 rst

Solution:

Multiply the coefficients 5 × 10 =50
Multiply the algebraic coefficients = pqr × rst = pqr²st

So, Product = 50pqr²st
The result of multiplication doesn't depend on the order in which multiplication is carried out.

Question 3: Multiply 20m × (10n + 3).

Solution:

Given: 20m x (10n + 3) 

Using the distributive laws,
= (20m × 10n) + (20m × 3)
= 200mn + 60m  

Question 4: Find the product 19p × (2q + 3z + 5pq)  

Solution:

Given: 19p × (2q + 3z + 5pq)  

Using the distributive law,
= (19p × 2q) + (19p × 3z) + (19p × 5pq)
= 38pq + 57pz + 95p²q

Question 5: Multiply (2x - 4y) and (3x - 5y).

Solution:

Given: (2x - 4y) × (3x - 5y)

Using the distributive laws,
[2x × (3x - 5y)] - [4y × (3x - 5y)]
[6x² - 10xy] - [12xy - 20y²]
6x² - 10xy - 12xy - 20y²
6x² - 20y² - 22xy 

Question 6: Multiply (2x + 4y) and (2x + y).

Solution:

Given: (2x + 4y) × (2x + y)

Using the distributive laws,
[2x × (2x + y)] + [4y × (2x + y)]
[4x² + 2xy] + [8xy + 4y²]
4x² + 2xy + 8xy + 4y²
4x² + 4y² + 10xy 

Question 7: Find the value of 3m (4m - 5) + 4 when m = 1

Solution

Given: 3m (4m - 5) + 4, m = 1
3m(4m - 5) = 12m² - 15m 

So, 3m (4m - 5) + 4 = 12m² - 15m + 4

Now put the value m = 1
= 12(1)² - 15 (1) + 4 
= 12 - 15 + 4
= 1

Question 8: Multiply (t - 5) and (3m + 5)

Solution: 

Given: (t - 5) × (3m + 5)

Using distributed law
t(3m + 5) - 5(3m + 5)
3tm + 5t - 15m - 25

Question 9: Multiply (z + 4) and (z - 4)

Solution: 

Given: (z + 4) × (z - 4)

Using distributed law
= z(z - 4) + 4(z - 4)
= z² - 4z + 4z - 16
= z² - 16

Question 10: Multiply (m - n) and (3m + 5n)

Solution: 

Given: (m - n) × (3m + 5n)

Using distributed law
= m(3m + 5n) - n(3m + 5n)
= 3m² + 5mn - 3mn - 5n²
= 3m² + 2mn - 5n²

Question 11: Simplify (m - n)(2m + 3n + r) 

Solution:

Given: (m - n)(2m + 3n + r) 

Using distributed law
= m(2m + 3n + r) - n(2m + 3n + r) 
= 2m² + 3mn + mr - 2mn - 3n² - nr
= 2m² + mn - 3n² + mr - nr

Question 12: Evaluate (p + q) (p + q + r)

Solution:

Given: (p + q)(p + q + r)

Using distributed law
= p(p + q + r) + q(p + q + r)
= p² + pq + pr + pq + q² + qr
= p² + q² + 2pq + pr + qr

Question 13: Evaluate (4 + 5t)(5 + 3t + q)

Solution

Given: (4 + 5t)(5 + 3t + q)

Using distributed law
= 4(5 + 3t + q) + 5t (5 + 3t + q)
= 20 + 12t + 4q + 25t + 15 t² + 5tq
= 15t² + 37t + 5tq + 4q + 20

Unsolved Practice Questions on Polynomial Mulitplication

1. Multiply 7xy × 3yz × 2xz
2. Find the product of 5pqr × 8rst
3. Multiply 15m × (7n + 4)
4. Find the product of 12a × (4b + 2c + 6ab)
5. Multiply (3x + 5y) and (2x − 4y)
6. Multiply (4x + 2y) and (3x − y)
7. Find the value of 2m(3m − 4) + 5 when = 2
8. Multiply (x−6) and (4y + 3)

Read More:

• Polynomials
• Polynomial Function
• Polynomial Formula